The invention relates to an improved internal combustion engine employing a free piston which reciprocates between oppositely located working chambers on an output shaft. Prior art engines of this type such as that shown in the Moore U.S. Pat. No. 1,389,453 have a piston with a square bore which interfits with a square portion of the output shaft to transmit rotary motion of piston to the output shaft. With designs of this type difficulty is encountered in sealing the square output shaft in the square piston bore and in providing a workable arrangement of rollers which ride the groove surface. The groove curvature of the prior art is generally limited to sinusoidal configurations.